1. Field of the Invention
The invention pertains to the field of flow porometry. More particularly, the invention pertains to methods and apparatus for the use of flow porometry to determine the pore structure characteristics of a filtration cartridge from measurements taken at specific locations along the cartridge length.
2. Description of Related Art
Filtration cartridges are workhorses of modern industry. Filtration cartridges are porous materials widely used for the separation of suspended solids from liquids and/or gases. Numerous applications of filtration cartridges are found in a wide range of industries, including biotechnology, chemical, pharmaceutical, food and drink, medical, electronic, automobile, and the construction industries. A wide variety of tasks are performed by filtration cartridges, such as, for example, filtration of bacteria, pollen and cells from bodily fluids, purification of chemicals, detoxification of waste water, removal of heavy ions from water for use in the electronic industry, purification of pharmaceutical products, removal of pathogens and solids from soft drinks, and removal of excess water from slurries.
The performance of a filtration cartridge and its ability to separate solids from fluids are governed by the pore structure characteristics of the complete filtration cartridge, rather than just the pore structure of the filtration media contained therein. Analysis of the pore structure characteristics of filtration cartridges is required for the evaluation of numerous filtration processes, including, for example estimation of filtration efficiency, evaluation of cartridge performance, and development of advanced and more efficient filtration media. Relevant pore structure characteristics include, for example, through pore throat diameters, bubble point (i.e., the largest through pore throat diameter), mean flow pore diameter, pore distribution, and permeability. Through pore throat diameter determines the sizes of particles that will be prevented from passing through the pore. The bubble point is the largest through pore throat diameter; it determines the smallest particle that cannot pass through the filter. Mean flow pore diameter yields the mean value of the pore diameter. Normally the majority of pores have diameters close to the mean flow pore diameter. It is also a measure of liquid and gas permeability. Pore distribution shows where an appreciable fraction of pores is present. It can be used to estimate efficiency. Permeability is a measure of the rate of the process.
All of the foregoing properties, relevant and important for filtration, can be measured by Capillary Flow Porometry, based on ASTM F-316. Capillary flow porometry is widely used for pore structure determination of filtration media (see e.g., Akshaya Jena and Krishna Gupta, Characterization of Pore Structure of Filtration Media, Fluid/Particle Separation Journal, Vol. 14, No. 3, 2002, pp. 227-241; Akshaya Jena and Krishna Gupta, Liquid Extrusion Techniques for Pore Structure Evaluation of Nonwovens, International Nonwovens Journal, Vol. 12, No. 3. 2003, pp. 45-53; and U.S. Pat. Nos. 6,766,257 and 6,684,685, the complete disclosures of which are hereby incorporated herein by reference in their entireties).
U.S. Pat. No. 6,684,685 discloses a liquid extrusion porosimeter and method for evaluating porosity characteristics (specifically, pore volume, pore distribution and liquid permeability) of porous materials, such as filtration media. The porosimeter includes a fluid reservoir located below the sample, and a penetrometer comprising a vessel that catches any fluid displaced from the reservoir of fluid, wherein a level of fluid rises in the penetrometer when additional fluid enters the penetrometer. The sample is preferably wetted, with the same type of fluid that is in the reservoir, prior to placing the sample on the porosimeter. The porosimeter preferably also includes a membrane located between the sample and the reservoir of fluid. The membrane has pores with a size smaller than any of the sample pores. Pore volume of the sample is determined by measuring the change in fluid level in the penetrometer after pressure, which is above the bubble point pressure of the sample but below the bubble point pressure of the membrane, is applied to the sample. Permeability is measured by measuring rate of flow while the liquid level is above the sample.
The PMI Capillary Flow Porometer is a completely automated instrument. It measures pressures of the test gas accurately. It increases pressure in small increments, allows the system to equilibrate, and then records the increase in pressure. The flow rate through the sample is also measured accurately. Pressures can be raised to high values or reduced from high values to very low values. The porometer delivers the compressed gas through a tube to the sample chamber, which can be designed to hold samples of various sizes and shapes.
The technique of flow porometry is based on the simple principle that a wetting liquid spontaneously fills the pores of filtration media. For the wetting liquid, the surface free energy of the filtration media with the liquid is less than the surface free energy of the filtration media with air. Therefore, filling of the pores by the wetting liquid is accompanied by a decrease in free energy and the filling process is spontaneous. The wetting liquid cannot spontaneously flow out of the pores, however, it can be removed from the pores by a pressurized non-reacting gas.
The gas pressure needed to displace a wetting liquid from a pore is related to the pore diameter, as follows:p=4γ cos θ/D  (1)where, p is the differential gas pressure on the wetting liquid in the pore, γ is the surface tension of the wetting liquid, θ is the contact angle of the wetting liquid with the filtration media, and D is the pore diameter. The test involves measurement of gas flow rates through a dry sample as a function of differential pressure. The differential pressure is reduced to zero, the sample is wetted with a wetting liquid, and gas flow rates through the wet sample are measured as a function of differential pressure.
The wet curve generated by the wet sample shows no gas flow with increase in differential pressure at the beginning of the test, because all of the pores are filled with the wetting liquid. The first pore to be emptied at the lowest pressure is the largest pore (see Equation 1 above). The differential pressure that initiates gas flow through a wet sample yields the largest through pore diameter.
The diameter of a pore can change along the pore path. The differential gas pressure that is sufficient to displace liquid from the pore throat can completely empty the pore and initiate gas flow. Therefore, the pore diameter computed from the measured differential pressure yields the through pore throat diameter. The measured largest pore diameter is the largest through pore throat diameter. The dry curve is produced by the dry sample. The half-dry curve represents computed data that yield half of the gas flow rate through the dry sample at a given differential pressure. The differential pressure at which the wet curve and the half-dry curve have the same flow rates yields the mean flow through pore throat diameter. The mean flow pore diameter is such that half of the flow is through pores smaller than the mean flow pore and the rest of the flow is through pores larger than the mean flow pore. The ratio of flow rates through the wet sample and the dry sample also yields flow distribution over pore diameter. This distribution has been shown to be close to pore fraction distribution (See A. K. Jena and K. M. Gupta, Pore Size Distribution in Porous Materials, Proceedings of International Conference Filtration 99, November 3-4, Chicago, INDA, 1999). Gas permeability is computed from measured gas flow rates through the dry sample using Darcy's law (See P. C. Carman, Flow of Gases through Porous Media, Academic Press, 1956).
Characteristics of filtration media that can be measured accurately by flow porometry include, for example, the constricted pore diameter, the largest pore diameter, the mean flow pore diameter, pore distribution, gas permeability, liquid permeability, envelope surface area and effects of operational variables, such as temperature, pressure, chemical environment and stress. Demonstrated applications of flow porometry include analysis of pore characteristics in the thickness direction, pore characteristics in the x-y plane, properties of individual layers of multi-layered products determined in-situ without separating the layers, and evaluation of properties without cutting samples and damaging the products. See, e.g., U.S. Pat. Nos. 6,766,257, 6,789,410, 6,845,651, and 7,040,141.
U.S. Pat. No. 6,766,257 discloses a method of determining the pore structure of the individual layers in a multi-layered composite porous material, including the steps of providing a sample of a multi-layered porous material, sealing the sample in suitable test chamber, filling the pores of the sample material with a wetting liquid, such that the liquid/sample surface free energy is less than the gas/sample surface free energy, using a non-reacting gas to apply pressure to one side of the sample sealed in the test chamber, increasing the gas pressure gradually, so as to displace the liquid from the pores, increasing gas flow through the sample, measuring the pressure at which liquid flows from each successive layer of the sample material, and calculating the pore structure using an equation selected from the group consisting of p=γ (dS/dV), D=4γ/p, and f=−d[100(Fw/Fd)]/dD.
U.S. Pat. No. 6,789,410 discloses a porosimeter that includes a pressurizable sample chamber with a membrane located directly below the sample. The membrane pores have a smaller size than any of the sample pores of interest. A fluid reservoir is located below the membrane such that the reservoir and the membrane form a seal. In operation, as fluid enters the fluid reservoir through the membrane or a reservoir inlet, fluid already in the fluid reservoir is displaced through a reservoir exit. An inlet in a fluid displacement reservoir receives the fluid displaced from the fluid reservoir. A recirculation line receives fluid from the exit of the fluid displacement reservoir and circulates the fluid into the inlet of the fluid reservoir. In a preferred embodiment, a pump recirculates the fluid through the recirculation line. Fluid returned to the reservoir circulates over the bottom of the membrane, and sweeps air bubbles out of the reservoir.
U.S. Pat. No. 6,845,651 discloses a method and apparatus for determining surface area and pore distribution of a sample. A pressurizable sample chamber of known volume holds a sample with unknown porosity characteristics. The sample chamber has a known pressure (or vacuum). A flow controller preferably controls the flow of the pure gas to be adsorbed by the sample in the sample chamber. A pressure monitor preferably monitors the pressure in the sample chamber. Once the pressure approaches a target pressure, the flow controller is closed. The pressure monitor continues to monitor the pressure until it stops changing when an equilibrium is attained. The amount of gas introduced into the system through the flow controller and the volume and final pressure of the sample chamber are used to calculate the amount of gas adsorbed. This calculation is subsequently used to determine the porosity characteristics of the sample. Some of these characteristics include, but are not limited to, pore distribution and surface area.
U.S. Pat. No. 7,040,141 discloses a method and apparatus for determining porosity characteristics of a sample having a plurality of pores, located within a pressurizable chamber. The sample divides the chamber into a first volume and a second volume. A known amount of vapor is introduced into the first volume and the second volume at the same pressure (PX). After equilibrium is reached, pressure and decrease in volume of vapor are measured. Pore diameter and pore volume are calculated. A pressure differential is created between the two volumes, and the pressure change is monitored after the pressure differential is introduced. In a preferred embodiment, the pressure is increased in the first volume by a small percentage (ΔPX), and the pressure change on both sides of the sample is monitored after the pressure increase. The flow rate of the vapor is calculated using the pressure change. These steps are preferably repeated. The pore distribution in the sample is preferably calculated from the flow rates.
Although there are known methods and apparatus for the analysis of pore structure characteristics of filtration media, one problem with the known methods is that they are not well-suited for analyzing the pore structure characteristics of complete filtration cartridges. Determination of pore structure of porous materials by porometry involves measurement of differential pressure of an inert gas and the flow rate of the gas through the pores. However, large and long industrial cartridges produce very high gas flow rates. When flow rates are high, it is difficult to prevent turbulence, accurately measure flow rates, detect small changes in flow rates, and accurately measure small changes in differential pressure. Consequently, it is difficult to determine the pore structure of many large cartridges.
The known methods and apparatus do not allow the pore structure characteristics of a complete filtration cartridge to be determined from measurements taken at specific locations along the cartridge length, and do not allow the pore structure of the cartridge to be evaluated as a function of cartridge length. Thus, there is a need in the art for a method and apparatus for using flow porometry to determine the pore structure characteristics of complete filtration cartridges and evaluate pore structure at different locations along the length of the cartridge and as a function of cartridge length.